direct driven permanent magnet synchronous generators with diode rectifiers for use in offshore wind...

7/30/2019 Direct Driven Permanent Magnet Synchronous Generators With Diode Rectifiers for Use in Offshore Wind Farms

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June 2007

Tore Marvin Undeland, ELKRAFT

Master of Science in Energy and EnvironmentSubmission date:

Supervisor:

Norwegian University of Science and Technology

Department of Electrical Power Engineering

Direct Driven Permanent MagnetSynchronous Generators with DiodeRectifiers for Use in Offshore WindTurbines

Tor Inge Reigstad


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Problem Description

The thesis is to focus on direct driven permanent magnet synchronous generators (PMSG) with

diode rectifiers for use in offshore wind turbines. Reactive compensation of the generator, powerlosses and control of the generator are to be studied. Configurations for power transmission toonshore point of common connection should also be considered. Costs, power losses, reliabilityand interface with the PMSG are to be discussed.

The purpose of the laboratory tests and simulations are to learn how a PMSG with diode rectifierbehaves. A 55kW PMSG is to be tested in Vindlabben, with and without reactive compensation.The generator current and generator voltage should be measured and the total harmonicdistribution (THD) of the current and the voltage are to be calculated. The results must becompared to simulations on an equal generator in PSCAD/EMTDC. A 2MW PMSG is also to besimulated to compare parallel and series compensation and to find how the generator efficiencyvaries with the wind speed. The generator is also to be simulated with constant DC-link voltageand varying local wind to find how much the turbine and generator efficiency decreases when aCluster step-up configuration is used. The DC-link voltage is in this case equal for parts of thewind farm or the whole wind farms. A 3MW ironless PMSG with very low synchronous reactanceshould finally be simulated to find how this generator behaves with a diode rectifier.

Assignment given: 15. January 2007Supervisor: Tore Marvin Undeland, ELKRAFT


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Abstract

This work is focused on direct-driven permanent magnets synchronous generators(PMSG) with diode rectifiers for use in offshore wind turbines. Reactive compensationof the generator, power losses and control of the generator are studied. Configurationsfor power transmission to onshore point of common connection are also considered.Costs, power losses, reliability and interface with the PMSG are discussed.

The purpose of the laboratory tests and simulations are to learn how a PMSG withdiode rectifier behaves. A 55kW PMSG is tested in Vindlabben, with and withoutreactive compensation. The generator current and generator voltage are measured andthe total harmonic distribution (THD) of the current and the voltage are calculated. Theresults are compared to simulations on an equal generator in PSCAD/EMTDC. A 2MW

PMSG is also simulated to compare parallel and series compensation and to find howthe generator efficiency varies with the wind speed. The generator is also simulatedwith constant DC-link voltage and varying local wind to find how much the turbineand generator efficiency decreases when a Cluster step-up configuration is used. TheDC-link voltage is in this case equal for parts of the wind farm or the whole wind farms.A 3MW ironless PMSG with very low synchronous reactance is simulated to find howthis generator behaves with a diode rectifier.

The laboratory tests and PSCAD simulations show that the maximal generatorpower increases when reactive compensation of the generator is used. The measuredand simulated generator voltage and current shapes are found to be approximatelyequal. Series compensated PMSGs have lower generator current rms and lower current

THD than parallel compensated PMSGs when the synchronous reactance is large.Therefore, the generator losses are 2 15% lower and the diode rectifier losses are0 1% lower, depending on the wind speed. The diode rectifier losses are lower than1%. The losses can be reduced even more if the diodes are connected in parallel. If aCluster step-up configuration is used, the turbine efficiency is reduced by 3 4%.

The ironless PMSG has a low synchronous reactance and reactive compensationis not needed because the reactive power produced by the generator is low. Parallelconnected capacitors have no positive effect and series connected capacitances mustbe very large and can therefore not be used. The generator current THD is very largewhen no reactive compensation is used. However, the current THD can be reduced by

connecting an inductance to the DC-link.Cluster step-up, two-step DC/DC system, turbine step-up and series connected

wind turbine are the most relevant layouts of the wind farms transmission systemdiscussed in this thesis. The cluster step-up system has low power losses since onlyone large DC/DC converter is used. Also, the power equipment in the turbine is veryreliable. However, the turbine efficiency is reduced since the generator torque andgenerator speed could not be controlled for one specific turbine. The other transmissionsystems require DC/DC converters in the turbines and they are therefore probably notas reliable. The total cost is crucial for the chose of the transmission system. Furthercost accountings for the different DC systems are needed.

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Preface

This report constitutes my Master Thesis spring 2007 and documents the work duringthe 10.th semester of my education at the Department of electrical power engineering,NTNU.

The laboratory tests and simulation performed during this work shows theadvantages and disadvantages of using a direct-driven PMSG with diode rectifier ina wind turbine. It also shows that the power losses of the generator is almost reducedto the minimum if series connected capacitors are used to deliver reactive power to thegenerator.

I want to thank my supervisors Prof. Tore Undeland and PhD. Thomas Fuglseth foruseful help and instructive conversations. I also want to thank Prof. Robert Nielsen foran enthusiastic discussion about permanent magnet generators, PhD. ystein Krveland Steinar Olsen for lending me the PM generator and the converter and helping mein Vindlabbenand Jon Are Wold Suul for useful help on my PSCAD related questions.

Trondheim, 12.June 2007

Tor Inge Reigstad

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Contents

1 Introduction 1

2 Grid connection of large offshore wind farms 32.1 High voltage DC (HVDC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 Voltage source converter (VSC) . . . . . . . . . . . . . . . . . . . . . 32.1.2 Line-commutated converter HVDC (LCC HVDC) . . . . . . . . . . 4

2.2 Wind farm layouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2.1 Series connected wind turbines . . . . . . . . . . . . . . . . . . . . . 52.2.2 Small DC wind farm . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2.3 Two-step DC/DC-converter system . . . . . . . . . . . . . . . . . . 62.2.4 Cluster step-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.5 Turbine step-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.6 Energy losses for the step-up configurations . . . . . . . . . . . . . 82.2.7 System efficiency of two step DC/DC wind farm . . . . . . . . . . 9

2.3 High voltage AC (HVAC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3.1 Components of the HVAC transmission solution . . . . . . . . . . . 112.3.2 HVAC transmission losses . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Comparison between HVAC and HVDC . . . . . . . . . . . . . . . . . . . . 122.4.1 Energy production cost of different wind farms . . . . . . . . . . . 132.4.2 Loss evaluation of HVAC and HVDC transmission solutions . . . . 15

2.5 Design criteria for offshore installations . . . . . . . . . . . . . . . . . . . . 18

3 PMSG and generator losses 193.1 PMSG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.2 Modelling of a PMSG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3 Harmonics and losses in the generator . . . . . . . . . . . . . . . . . . . . . 21

4 PMSG with diode rectifier 234.1 PMSG with active rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2 Three-phase, full bridge diode rectifier . . . . . . . . . . . . . . . . . . . . . 244.3 PMSG with diode rectifier and series compensation . . . . . . . . . . . . . 24

4.4 PMSG with diode rectifier and parallel compensation . . . . . . . . . . . . 344.5 Passive filters for reducing current harmonics . . . . . . . . . . . . . . . . . 414.6 Active shunt filter for reducing current harmonics . . . . . . . . . . . . . . 44

5 Control systems 475.1 Speed and torque control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.1.1 MPPT with knowledge of the turbine characteristic . . . . . . . . . 485.1.2 MPPT without knowledge of the optimal turbine characteristic . . 495.1.3 Comparison between the control strategies . . . . . . . . . . . . . . 49

5.2 Fixed DC-link voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

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6 Modelling of the wind turbine 516.1 Permanent magnet synchronous generator . . . . . . . . . . . . . . . . . . 51

6.2 Diode rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516.3 The inertia of the wind turbine . . . . . . . . . . . . . . . . . . . . . . . . . 536.4 Control system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6.4.1 Pitch controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546.4.2 Speed controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546.4.3 Calculation of optimal turbine rotation speed . . . . . . . . . . . . . 556.4.4 Load current controller . . . . . . . . . . . . . . . . . . . . . . . . . 55

7 Simulations and laboratory tests of a 55 kW radial PMSG 577.1 Generator frequency at 50 Hz . . . . . . . . . . . . . . . . . . . . . . . . . . 60

7.1.1 Measurements with reactive compensation . . . . . . . . . . . . . . 607.1.2 Simulations with reactive compensation . . . . . . . . . . . . . . . . 617.1.3 Measurements without reactive compensation . . . . . . . . . . . . 657.1.4 Simulations without reactive compensation . . . . . . . . . . . . . . 66

7.2 Generator frequency at 27.5 Hz . . . . . . . . . . . . . . . . . . . . . . . . . 697.2.1 Measurements with reactive compensation . . . . . . . . . . . . . . 697.2.2 Simulations with reactive compensation . . . . . . . . . . . . . . . . 737.2.3 Measurements without reactive compensation . . . . . . . . . . . . 737.2.4 Simulations without reactive compensation . . . . . . . . . . . . . . 74

7.3 Series compensated PMGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

8 Simulation of a 2 MW wind turbine with radial PMSG 838.1 Efficiency for parallel compensated PMSG, series compensated PMSG

and PMSG with ideal load . . . . . . . . . . . . . . . . . . . . . . . . . . . . 838.2 Simulation of WECS with constant DC-link voltage . . . . . . . . . . . . . 87

8.2.1 Parallel compensated PMSG and 9m/s average wind speed . . . . 878.2.2 6m/s average wind speed . . . . . . . . . . . . . . . . . . . . . . . . 898.2.3 9m/s average wind speed . . . . . . . . . . . . . . . . . . . . . . . . 928.2.4 12m/s average wind speed . . . . . . . . . . . . . . . . . . . . . . . 958.2.5 Power efficiency of WECS with constant DC-link voltage . . . . . . 97

9 Simulation of a 3 MW ironless PMSG 99

10 Discussion and conclusion 10510.1 AC or DC offshore grid? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10510.2 Series or parallel compensated PMSG? . . . . . . . . . . . . . . . . . . . . . 10510.3 Laboratory tests of a 55kW PMSG . . . . . . . . . . . . . . . . . . . . . . . . 10710.4 Layouts of DC grid wind farms . . . . . . . . . . . . . . . . . . . . . . . . . 10710.5 Ironless PMSG with diode rectifier . . . . . . . . . . . . . . . . . . . . . . . 10810.6 Diode or IGBT rectifier? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10910.7 Further work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

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Offshore Wind Turbines, Tor Inge Reigstad

1 Introduction

Floating wind turbines are an exciting area of research with lot of challenges. Someof these challenges are considered in this report. The thesis focuses on configurationsfor power transmission from the turbine generator to onshore. Most attention is givento the generator diode rectifier and how this rectifier affects the permanent magnetsynchronous generator and the generator losses. The reliability of the turbines will bemuch better if a diode rectifier is used instead of an IGBT rectifier. Different offshoregrid configurations are also considered compared, both AC and DC. The aim has beento find a simple, inexpensive, reliably and low losses transmission system which is fittedfor the PMSG with diode rectifier.

Essential theory is present in Chapter 2 to 5. Transmission systems for large offshorewind farms will be reviewed in Chapter 2 to get overall view of the system. Differentways of integrating the turbine generators in the transmission system is present.Chapter 3 presents the permanent magnet synchronous generator, how the generatoris modelled and how the generator losses are calculated. The PMSG with diode rectifierand reactive compensation of the generator are examined in Chapter 4. At last, thedifferent control system of the generator is present in Chapter 5.

Chapters 6 to 9 present the results of the laboratory work and the simulations inPSCAD/EMTDC. Some results are discussed in this chapter. The modelling of theturbine, PMSG, diode rectifier and controllers in PSCAD is explained in Chapter 6.Turbine, generator and diode rectifier data is also found in this Chapter.

The laboratory work on the 55kW PMSG is present in Chapter 7. The generator

is also simulated in PSCAD/EMTDC and the results are compared to the laboratorymeasurements. The simulations are performed with parallel reactive compensation ofthe generator, series compensation and no compensation while the generator is testedwith parallel compensation and without reactive compensation.

In Chapter 8 simulations of a 2MW turbine is presents. Series reactive compensationis compared to parallel reactive compensation to find what methods which are bestfitted for wind turbines. The generator system is also simulated with constant DC-linkvoltage to find how much the turbine and generator efficiency decrease if a cluster step-up configuration is used.

Simulations of a 3MW ironless PMSG is present in Chapter 9. The ironless generators

have a lower synchronous reactance and the simulations are performed to se how thisaffects the use of diode rectifier.

General discussions are presents in Chapter 10. The chapter also summarize thethesis and draws general conclusions. MatLab-code, some PSCAD-files and somecalculations performed in Excel are found on the CD attached to the report. The PSCAS-files and the Excel-files are not user-friendly, but could be a help for people who wantto continue my work. The files are sorted by the chapter they are presented in.

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1 INTRODUCTION

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2 Grid connection of large offshore wind farms

In this section, different layouts for large offshore grid connections are discussed.Economic and energy efficiency of commercial solutions used today and alternativesolutions are considered. In [27] and [28], layouts of various large-scale wind farms,using both HVAC as well as HVDC, are investigated. The criteria in this investigationis the energy production cost, which is defined as the total investment cost divided bythe total energy production of the wind farm.

2.1 High voltage DC (HVDC)

HVDC transmission may be the only feasible option for connection of a wind farm

if the distance exceeds 100-150 km. HVDC transmission offers many advantages forintegration of large offshore wind farms:

The power follow is fully defined and controlled.

Faults on one AC network will not directly affect the AC voltage on the othernetworks because the networks are decoupled by the asynchronous connection.

There is no technical limit on the transmission distance with a DC cable, as it is forAC cables.

A pair of DC cable can carry up to 1600 MW.

The cable power loss is lower than an equivalent AC cable [15]

It is often difficult to find suitable grid connection point. If HVDC is used, the powercould be directed to a stronger grid connection point with minimal increase in costand transmission losses. It might also be necessary to use DC-cables for the onshoretransmission, because it could be difficult to get permission to build new over-headlines. [27]

2.1.1 Voltage source converter (VSC)There are two main HVDC transmission technologies: voltage source converter (VSC)using IGBTs and line-commutated converter HVDC (LCC) using thyristors.

VSC is self-commutating and it does not require an external voltage source for itsoperation. The reactive power can be controlled by the power converters and it isindependent of the active power control. Power can be transported to the wind farmwhen necessary and the AC voltages on both sides can be controlled. No AC harmonicfilters for reactive power control are needed. However, VSC transmission does havehigher power loss compared with a LCC HVDC system. Typically, the total losses atfull load for the two converters are about 3.5% for VSC and 1.5% for LCC HVDC. [15]

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2 GRID CONNECTION OF LARGE OFFSHORE WIND FARMS

Figure 1 shows the single-line diagram for a VSC transmission system with DFIGgenerators. A three-level neutral point clamped converter is used instead of a two-level

converter, resulting in lower power losses. [15]

Figure 1: Single-line diagram of wind farm connection using VSC transmission. [15]

The advantages of HVDC VSC solutions are based on its capability to supply andabsorb reactive power and to support power system stability. The disadvantage is thatground faults can be problematic. Main components of the transmission system basedon VSC devices are; VSC converter station circuit breaker, system side harmonic filter,interface transformer, converter side harmonic filter, VSC unit, VSC DC capacitor, DC

harmonic filter, DC reactor, DC cable or overhead transmission line and auxiliary powerset. [18]

2.1.2 Line-commutated converter HVDC (LCC HVDC)

Line Commutated Converter (LCC) based transmission systems with thyristors havebeen successfully installed all over the world. LCC HVDC can be used for higher powerlevels than VSC. Power levels up to 1600 MW are available pr 2005. However, a LCCHVDC converter station occupies twice the area of a VSC transmission station. It isalso necessary to provide a commutation voltage in order for the offshore LCC HVDCconverter to work properly. Another draw back of this transmission solution is therequired reactive power to the thyristor valves in the converter and the generation ofharmonics. Filters and switchgear is therefore needed. Alternatively, a STATCOM couldbe used. This technology is very large in physical size, and the transistor technology isalso more attractive due to the better controllability of the reactive power. [15] [18]

Main components of the transmission system base on LCC devices are; AC and DCfilters, converter transformer, converter based on thyristor valves, smoothing reactor,capacitor banks or STATCOM, DC cable and return path, auxiliary power set andprotection and control devises. [18]

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2.2 Wind farm layouts

In this section different DC wind farm layouts are considered

2.2.1 Series connected wind turbines

Figure 2: The layout of series-connected wind turbines with a DC output voltage [28]

Figure 2 shows a general layout of a wind farm with series connected wind turbines.There are two major advantages with this solution: no offshore platform is used andhigh voltage DC is used to bring the energy to shore. The transformers will be smallerand thus possibly cheaper compared to the systems of today, while the cost for the

higher isolation at the output of the turbines will be higher. The total cost of the electricalsystem will probably be lower for the proposed system, according to [28]. For a 160 MWwind farm located at 55 km from a suitable grid connection point, this solution shows apotential of 8% cost reduction. [28]

The benefit of this system is that it, in spite of a relatively large possible size,does not require large DC-transformers and offshore platforms. The drawback withthis configuration is that the DC/DC converters in the wind turbines must have thecapability to operate towards a very high voltage.

A system with series connected wind turbines and synchronous generators donot need traditional components, such as gear boxes and local wind turbine 50 Hztransformers, which are related to major problems. There are fewer problems relatedto power electronics. If a diode rectifier is used instead of an IGBT rectifier to rectify thepower from the generator, the power electronics will be even more reliable. [28]

2.2.2 Small DC wind farm

Figure 3 shows the electrical system for a small DC wind farm. The electrical systemis identical to the system of the small AC wind farm. The only difference is that thetransformer in the wind farm grid interface is replaced with a DC transformer and aninverter. Also, a rectifier is needed for each wind turbine, but no offshore platform isneeded.

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Figure 3: DC electrical system with series connected wind turbines [27]

2.2.3 Two-step DC/DC-converter system

In general, the DC-grid consists of several clusters, which are connected either inparallel or in series. Since the difference between the output power of each turbineand the total power transferred to the shore is huge, several voltage steps are preferred.Otherwise, either the generators must be designed for extremely high voltages or thetransmission losses are increased significantly. A DC/DC converter could be used forstepping up the voltage. [6]

Figure 4: Schematic scheme for a two step-up configuration [6]

The voltage step up can be done in different places. Figure 4 shows the schematicscheme for a two step-up configuration. It uses two DC/DC-converter system, onesystem is stepping up the voltage after each turbine, up to a medium-voltage level. Thepower from many turbines is collected and the voltage is stepped up to the transmissionlevel. An advantage of this system is the direct step-up of the voltage after the turbinewhich leads to reduced cable losses at the distribution level. The DC-link voltage ateach turbine could also be controlled individually. However, the additional DC/DC-converter leads to extra losses and investment cost. [6]

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Figure 5: Schematic scheme for a Closter step-up configuration [6]

2.2.4 Cluster step-up

The second system is called a one Cluster step-up system and is shown in Figure 5.The DC-power from the generators is collected on an offshore platform and afterwardsa large converter system is stepping up the voltage to the transmission level. Theadvantage of this system is that the number of converters is minimized and that a largeconverter has a higher efficiency. Since only two voltage levels are used, the distributionlevel strongly depends on the generator voltage, which today is limited to 5 kV line-to-line. [6] This system has a disadvantage if a variable speed PMSG with diode rectifier isused because the DC-link voltage could not be regulated individually for each turbine.

Therefore the DC-link voltage will be the same for all turbines and the turbine rotationspeed will not be ideal. The power will vary some with the turbine rotation speed.If the wind speed is more or less equal for the whole Cluster-area, this will not be alarge problem. The DC-link voltage could in this case be regulated in such way that theturbines keep the optimal rotation speed for the average wind speed of all turbines.

2.2.5 Turbine step-up

Figure 6: Schematic scheme for a Turbine step-up configuration [6]

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The last system, the turbine step-up system shown in Figure 6, has DC/DCconverters connected directly to each turbine. Only two voltage levels are used and

the distribution level is reduced because of the high voltage. No offshore platforms arerequired. However, the DC/DC converter has to be designed for a low power level,which could reduce the efficiency of the converter. [6]

2.2.6 Energy losses for the step-up configurations

Figure 7: Power losses for different configurations of the DC-grid [6]

Figure 7 shows the losses of these three configurations for different DC-voltagelevels. The wind farm size is 500 MW, the losses for the DC/DC converters werecalculated analytically in [6] by using values from datasheets for the semiconductorsand an additional loss model was used to find the transformer losses. The difference in

losses does not vary significantly when the DC-link voltage changes. The figure showsthat the Cluster step-up solution has the lowest losses. However, as seen, there are somedisadvantages when this configuration is used in a variable speed PMSG applicationwith diode rectifier. The Turbine step-up solution is the next best solution, but the lossesare over twice as big as for the Cluster step-up solution. [6]

The main reason why the Cluster step-up solution has the lowest losses is that thedistances are quit short within the wind farm. Therefore, it is not necessary to havea large internal DC voltage. Since a large converter has a higher efficiency, the powershould be collected before the voltage is raised. The high output voltage of the turbinestep-up solution and the low power level result in large losses for this solution. The

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two-step-up solution has even more losses due to the use of two DC/DC-converters,one of them with low power level. [6]

2.2.7 System efficiency of two step DC/DC wind farm

System efficiency of a two step DC/DC wind farm layout is investigated in [14]. Threedifferent converters have been compared; the fullbridge converter with phase shiftcontrol (FB), the single active bridge converter (SAB) and the series parallel resonantconverter (LCC). [14]

Figure 8: Typology for the fullbridge converter using phase shift control [14]

Figure 9: Typology for the single active bridge converter [14]

The typology of the fullbridge converter using phase shift control is shown in Figure8. This converter has a significantly lowered performance when handling variations inthe voltage and power. The output is current-stiff. A single active bridge converter inFigure 9 looks similar to the fullbridge converter. However, the control is different theoutput filter creates a voltage-stiff output. The series parallel resonant converter, shownin Figure 10, has lower switching losses because it switches at zero current and/or zerovoltage. This is why this type of converter often has the lowest power loss. [14]

Two different control strategies are evaluated. In the first strategy (1) the DC/DCconverter in the wind turbines handles all voltage variations. The input voltage of thefirst converter is 2-5 kV while the output voltage is 15 kV. In the second strategy (2) the

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Figure 10: Typology for the series parallel resonant converter [14]

DC/DC converters in the wind turbines only handle the variations between the wind

turbines in the same group and the group DC/DC converter handles the variationsbetween the groups. The input voltage of the first converter is 2-5 kV while the outputvoltage is 6-15 kV. [14]

Table 1: Average losses for the two control strategies and the three types of convertersat different wind speeds [14]

Table 1 shows the average losses for the two different control strategies and for thethree different converters. It becomes obvious that the power loss is less with the seriesparallel resonant converter. The first control strategy with constant output voltage of thefirst converter has the lowest total converter losses, 2.4%. The loss of the second controlstrategy is 2.8%. The solution with constant transformation on the second converter istherefore preferable. [14]

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2.3 High voltage AC (HVAC)

According to [15], HVAC will be used for most wind farm application with a connectionlength off less than 50-75 km because this is the simplest and most economic gridconnection method. If the connection distance exceeds 50 km, dynamic reactive powercompensation may be required when the HVAC solution is used. [15]

2.3.1 Components of the HVAC transmission solution

The voltage level within an offshore wind farm grid is typically in the range of 30-36kV. Therefore a substation is necessary for a large wind farm, to step up the voltage forthe transmission to shore. A HVAC transmission system also needs; HVAC submarinetransmission cables, offshore transformers, compensation units like thyristor controlledreactors (TCR) both offshore and onshore and, depending on the grid voltage, onshoretransformers. [18]

2.3.2 HVAC transmission losses

Table 2: Transmission losses of 500 MW wind farm with 9 m/s average wind speed (inpercent) [18]

Table 3: Transmission losses of 1000 MW wind farm with 9 m/s average wind speed (inpercent) [18]

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Tables 2 and 3 show the transmission losses of wind farms with 9 m/s average windspeed for respectively 500 MW and 1000 MW rated power. The loss is given in percents

of the annual wind farm production. As seen, the losses are lowest for the 400 kVsolutions in both cases as long as the cable length is below 150-200 km. For larger cablelengths, the voltage level has to be reduced, as shown in Figure 14. This is explained inChapter 2.4.2. [18]

Figure 11: Participation of each transmission component in total transmission losses for500 MW wind farm, 9 m/s of average wind speed, at 100 km transmission distance,three three-core 132 kV submarine cables [12]

Figure 11 shows the share each transmission component contributes to the totaltransmission losses for a 500 MW wind farm with a transmission distance of 100 kmusing a 132 kV cable. As seen from the figure, the cable losses represent the highestshare of the total transmission losses. Thus, in order to decrease the total transmissionlosses, special attention should be given to the cable selection. [18]

2.4 Comparison between HVAC and HVDC

Using conventional HVDC transmission offers many advantages to an AC connection.

Transmission distance is not a technical limitation since the transmission distanceusing HVDC is not affected by cable charging current [21] [20]

Frequency at sending end can be variable and the sending and receiving endfrequencies are independent [21] [20]

Offshore installation is isolated from mainland disturbances [21]

Power flow is fully defined and controllable [21]

Proven and reliable equipment [21]

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Low cable power loss, due to no affects of cable charging current. [21]

High power transmission capability for each cable. A pair of HVDC lines maycarry 1.7 times the power of a similar sized AC line. [21]

Many factors influence whether HVAC or HVDC should be used. Kirky suggestsin [20] that conventional HVDC will be the optimal solution when the distanceoffshore is greater than approximately 100 km and the wind farm size is greaterthan approximately 350 MW. HVDC could also be used when the connection into theAC network is at a weak point or a significant length AC transmission line onshoreis needed to reach a suitable AC network connection point. The HVDC control of

power may also assist in recovery, limit the effect or even correct the instability afterdifferent fault conditions. Therefore HVDC can be used where AC network studies andsimulation show unstable behaviour. [20]

The high cost of the associated AC-DC converter infrastructure, offshore platformspace and switching losses has generally limited the attractiveness of HVDC to verylarge installation located a long distance offshore. [1] As wind farms become larger andthe distant from shore increases, the justification for using HVDC to transmit the powerto the onshore network becomes easier, particularly at power levels of 500 MW or more.For larger wind farms, the cost of the converter stations and platforms per MW willbecome less. Existing voltage sourced converter (VSC) transmission technology can notoffer an economical solution at this power level due to the high cost of the multipleconverters and cables that are required. [20]

2.4.1 Energy production cost of different wind farms

Lundberg has analysed the economics of different wind farm layouts in his Phd. Thesis.Figure 12 shows the normalized energy production cost of the different 160 MW windfarms as function of the transmission distance. As seen, the series DC solution is theleast expensive for all transmission length larger than 10 km. An increased investmentcost of 13% can be allowed for the series DC park before the production cost becomes

equal to the large AC park, according to [28].The work done in [28] also shows that the energy production cost is strongly

dependent on the average wind speed. As an example, the energy production costat an average wind speed of 6.5m/s was twice as high as the cost for an average windspeed of 10m/s. It was also found that the energy production cost decreases when thepower of the wind farm increases. [27] This is an important reason to build offshorewind parks.

Figure 13 shows the cost of the AC and DC cables per km as a function of the ratedpower. It can be noted that the DC cables are much cheaper than the AC cables for thesame rating.

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Figure 12: The normalized energy production cost of the different 160 MW wind farmsas function of the transmission distance and at an average wind speed of 10 m/s [28]

Figure 13: Cost of AC and DC cables per km [27]

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Figure 14: Transmission capacity of different HVAC transmission cables for threevoltage levels, 132, 220 and 400 kV. [18]

2.4.2 Loss evaluation of HVAC and HVDC transmission solutions

In [18], losses for HVAC and HVDC transmission solutions for large offshore wind

farms are compared. If HVAC cables are used, the transmission distance would belimited. A comparison of the transmission capacity of different cable operated at certainvoltage levels (132, 220 and 400 kV) and different compensation solutions (only onshoreor at both ends) is presented in Figure 14. The critical distance is achieved when halfof the reactive current produced by the cable reaches nominal current at the end of onecable; 370 km, 281 km and 202 km for respectively 132 kV, 220 kV and 400 kV. [18]

Table 4: Transmission losses for different HVDC LCC converter station layouts with 9m/s average wind speed (in percent) [18]

Three different HVDC LCC layout are considered for a 500 MW wind farm and fourfor a 1000 MW wind farm in [18]. Loss model and assumptions are also given here.

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The transmission losses are given Table 4. When this table is compared to Tables 2 and3 it becomes obvious that the transmission losses are much lower for a HVDC LCC

solution than a HVAC solution. The total HVDC losses are about one fourth of theHVAC transmission losses for 200 km cable length. [18]

Figure 15: Loss participation for the HVDC LCC system losses. [18]

Loss participation of each component in the system for some configurations is shownin Figure 15. Converter stations are responsible for the highest share of the overallsystem losses. The participation of the cable increases with cable lengths.

Figure 16 shows the conclusion; HVAC has lowest losses for transmission length lessthan 55-70 km. The losses in this area depend mostly on the distance to the shore. Forlarger transmission lengths, the HVDC LCC solution has the lowest losses. As seen fromthe figure, the losses in this area also vary with the wind farm rated output power. The

tendency is that percent loss decrease when the size of the wind farm increase, but theloss percent will also depend on the converter station layout. The HVDC VSC solutionhas higher losses than the HVDC LCC solution for all power outputs, and are thereforenot shown in Figure 16. [18]

In [18], three different HVDC VSC layout are considered for a 500 MW wind farmand two for a 1000 MW wind farm. Loss model and assumptions are given in [18]. Thetransmission losses are given Table 5. When this table is compared to Table 4 it becomesobvious that the transmission losses are over twice as high for the VSC solution than forthe HVDC LCC solution. Figure 17 shows that the converter stations contribute most tothe overall system losses and that the share of cable losses increases with length. [18]

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Figure 16: MW-km plane, comparison HVAC-HVDC LCC for different wind farm sizeand different distances to shore [18]

Table 5: Transmission losses for different converter station layouts with 9 m/s averagewind speed (in percent) [18]

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Figure 17: Loss participation for the HVDC VSC system losses. [18]

2.5 Design criteria for offshore installations

Offshore equipment is exposed to extreme weather, salt and moist air and should bedesigned for these circumstances and the equipment must be located indoors or insealed enclosures. Equipment should be as compact as possible, to reduce the overallsize and weight and thereby the construction cost. Multistorey structure can be used.It should also have high reliability and should be as simple as possible with longmaintenance intervals or preferably no maintenance at all. [20]

Some form of UPS, generator, battery or a combination of these is needed to ensurepower supply when there is no wind. Load should therefore be graded into essentialand non-essential. AC busbar voltage should also be as low as possible to reduce ACharmonic filter and switchgear size.

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3 PMSG and generator losses

3.1 PMSG

A direct driven permanent magnet synchronous generator is lighter and more reliablethan the traditional solution with an asynchronous generator and a gear. The gear needsmaintains and is very heavy. Both weight and reliability are important for offshorefloating wind turbines. A light nacelle means less force on the tower. The tower and thefloating structure can therefore be made cheaper. Good reliability is important becauseit is difficult and expensive to access the turbines.

Figure 18: Comparison of the diameter of active material in radial and axial machines

[33]

There are generally three types of permanent magnet machines; radial, axial andtransversal flux machines. The radial flux machine (RFPM) is the classic type and themost common. The rotor can have buried or surface mounted magnets and the boththe stator windings and tooth shape are quit similar to other AC-machines. The activematerials, such as copper, magnets, iron and sheet metal is the material converting themechanical energy to electrical. These are place along the air gap. In wind turbinesthe generator diameter is large and thereby the layer with active material is pretty thin.Since the radius is large, the torque will also be large. [33]

Axial flux machines (AFPM) is magnetized in the axial direction, as shown in Figure18. Given the same outer diameter and the same force per area in the air gap, the AFPMhas a lower torque per volume of active material due to the fact that much of the forceis working in a smaller radius and thus producing less torque. However, the volume ofthe machine can be reduced because the power density (W/m3) is higher. The AFPMusually has a large diameter and a short length. The generator has a disc shaped designand these discs can be connected in series. As for RFPM the rotor in an AFPM can bemade with surface mounted or buried magnets. [33]

The third machine is the most complex and least equal to classic machine design,the transversal flux machine (TFPM). It can be single sided or double sided respectively

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3 PMSG AND GENERATOR LOSSES

with one or two wound rings of copper with iron cores to lead the magnetic flux aroundthe copper. The permanent magnets can be either buried or surface mounted. The

machine has very high force and power density, and is therefore ideal for high torque,low speed applications, such as wind turbines. To achieve this high power density, thesynchronous reactance becomes very high, which makes the converter expensive. TheTFPM itself can also be expensive due to the complex design and many parts. [33]

3.2 Modelling of a PMSG

The permanent magnet synchronous generator is modelled in a d-q-o reference framefixed to the rotor. Equation (1) and (2) are found in [9]. Equation (1) shows the stator

voltage equations and Equation (2) shows the flux linkage equations. The dampingwindings are replaced with two equivalent windings D in direct and Q in quadratureaxis. Figure 19 shows the schematic model. The electromagnetic torque is given byEquation (3). The simulink model is found in [9].

Figure 19: Schematic of the transformed model for PM synchronous machine in thed-q-0 reference frame [9]

usd = Rsisd +

dsddt

rsq

usq = Rsisq +

dsq

dt+r

sw

us0 = Rsis0 +

ds0dt

uD = RsiD +dD

dt

uQ = RsiQ +dQ

dt

(1)

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s

d = Ldi

s

d + MfIf + MDiDsq = Lqi

sq + MQ IQ

s0 = L0i0f = LfIf

D = LDiD + Mf D If + MDisd

Q = LDiQ + MQisq

(2)

Te =3

2P

sdi

sq sqisd

(3)

The model takes into account the iron losses as well as the parameters variationwith the operating temperature. The temperature depends on the rotor speed [9]

3.3 Harmonics and losses in the generator

The total harmonic distortion (THD) describes the content of harmonics in a voltage orcurrent waveform. A low THD means the first harmonic is dominating and the contentof higher harmonics is low. This is normally preferred since only the first harmonic iscontributing to power production, while higher harmonics causes losses. The THD inthe current is define in Equation (4). Is1 is the first harmonic of the current and Ish is the

hth harmonic of the current. [22]

THDi =

h=1(Ish Is1)

2 (4)

Harmonic currents in the stator cause losses in the generator. Basically the totalpower losses generated in the permanent machine can be divided into two groups;copper losses and core losses. The copper losses (Pcu) are produced in the stator windingand depend on the RMS current. This is shown in Equation (5). Iai is the RMS value of

the ith harmonic component of the current Ia and Ra is the stator equivalent resistance.When the current level increases, the temperature increases and so the stator resistanceRa. This effect is not included in the calculations. [26]

PCU = 3Ra

i=1

I2ai (5)

Equations (4) and (5) show that the copper power losses are proportional to 1 +THD. If a diode rectifier is used to rectify the voltage from a permanent magnetsynchronous generator, the THD of the current may be about 0.30, resulting in 30%larger copper power loss than the case with no current harmonics. The harmonicscauses high frequency flux changing, causing hysteresis (Ph) and eddy current power

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3 PMSG AND GENERATOR LOSSES

losses (Pe). The total core losses are given by Equation (6). Equations (7) and (8) showthe hysteresis and eddy current power losses when the harmonics of the voltage are

known. [26]

Pcore = Pe + Ph =

kef2B2max + khf B

2max

Weight (6)

PePe1

i=1

ViV1

2(7)

PhPh1

i=1

ViV1

2 1i

(8)

ke and kh are constants, Bmax is peak flux density, f is the rated frequency, weightrepresents the core and copper weight, Ph1, Pe1 and V1 are the hysteresis losses, eddycurrent losses and the line to line output voltage respectively at the nominal conditionresistive load without harmonics. These equations show that the core losses increasewhen the voltage harmonics increase. [26]

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4 PMSG with diode rectifier

In this chapter, a solution with a PMSG with diode rectifier is considered. When a dioderectifier is used, special attention on the reactive power from the rectifier, power supportto the generator and on the low order harmonics created by the diode rectifier is needed.The low orders harmonic can create ripple in both the torque produced by the generatorand in the power after the rectifier. The number of phases in the generator can reducethe impact of the harmonics. Filters can also be placed between the generator and therectifier. A DC/DC converter is used to control the DC-link voltage, and thereby thetorque of the PM generator with diode rectifier. The DC-link voltage is controlled bycontrolling the current going into the DC/DC converter. [28]

4.1 PMSG with active rectifier

A solution with a diode bridge rectifier is much simpler and more reliable than asolution with IGBTs. However, the stator flux can not be controlled. [16] suggest thatthe generator volume is almost doubled compared to using an active rectifier.

Figure 20: Principal scheme of the 2MW DC wind turbine with full variable speed andIGBT rectifier [28]

Figure 20 shows a principal scheme of a permanent magnet generator with IGBTrectifier and a DC/DC converter. The benefit with the IGBT rectifier is that the torqueof the generator, the generator currents, stator flux and active and reactive power tothe generator can easily be controlled. Since the generator current can be controlled for

maximum torque output, the generator size, weight and cost can be minimized. It isalso easy to obtain a smooth torque, a desirable flux level in the generator and a goodquality of the DC-link voltage. [16] [28]

Any type of generator can be used since the reactive power can be controlled.Another advantage of the IGBT rectifier is that it keeps the input voltage to the DC/DCconverter constant. The DC/DC converter can therefore be optimized because itoperates as a constant ratio DC transformer in normal operations. However, these activerectifiers are both expensive and subject to failure. Reliability is important for offshoreapplications since maintenance and repair is extremely expensive and the access to theturbines is difficult in bad weather conditions. [16] [28]

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4 PMSG WITH DIODE RECTIFIER

Figure 21: 3-level IGBT converter efficiency. [17]

Figure 21 shows the IGBT rectifier efficiency for a 50kW converter for wind powerapplications. The losses is about 2% for rated power, and the efficiency of the converterdecreases when the power level decrease.

4.2 Three-phase, full bridge diode rectifier

A three-phase, full-bridge diode rectifier is shown in Figure 22. The inductors Ls is inthis case the synchronous reactance of the permanent magnet synchronous generator.The DC-link voltage is found from Equation (9). VLL is the line-to-line induced voltagein the generator, Id is the phase current and Vd is the voltage drop on the DC-linkcaused by the synchronous reactance. As seen from this equation, the DC-link voltagewill decrease when the current in the machine increase, or the current will increasewhen the DC-link voltage decrease. Thereby, the DC-link voltage can be used to controlthe machine current and the machine power.

Vd = Vdo Vd = 1.35VLL 3Ls Id (9)

4.3 PMSG with diode rectifier and series compensation

The generator could be equipped with phase compensating capacitors, in series withthe stator windings, as shown in Figure 24. If a diode rectifier is used to rectify thepower from a permanent magnet generator, the load power angle is always zero, andcan not be controlled. Figure 23 shows the phasor diagram for a series compensatedgenerator. The load voltage Uload is in phase with the generator current I. To have a

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Figure 22: Three-phase, full-brigde rectifier [22]

Figure 23: The phasor diagram for the series-compensated generator, drawn for onespecific compensation. [3]

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maximum power output from the generator, the current I has to be in phase with theinduced voltage EPM . The size of the capacitor has to be chosen so that this fits for the

highest rotation speeds and the maximal power.Series compensation has the advantage that the reactive power produced by the

compensation follows the variations in the generators reactive power consumption, asthe generator currents changes. However, the compensation level change when thegenerator speed change since the inductance reactance decrease when the generatorspeed decrease, and the capacitor reactance increase when the generator speed decrease.This is shown in Equation (10). [3]

Uload = EPM j (Lm + L) I+ RI+I

jC= EPM

jLI+ RI+

I

jC

(10)

EPM is the induced voltage in the generator, Uload is the generator output voltage, Iis the generator current, R is the stator resistance, Lm is the magnetising inductance, Lis the leakage inductance, L is the total inductance and is the electrical frequency.

The total impedance of the generator synchronous reactance and the serie connectedcapacitance is given by Equation (11). As seen, the capacitance needs to be quite highto make the total impedance zero. If the capacitance is to low, the generator will beovercompensated.

Xtotal = L1

C=

L 1

2C

(11)

Figure 24: The series compensated generator with diode rectifier [3]

The emfePM , shown in Figur 24, is the no-load voltage, produced by the permanentmagnets and depends on the generator speed. e is the voltage induced by the air gap

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Figure 25: Phasor diagram for different compensation: A) no 0% B) half 50% C) full100% D) overcompensated 133% [3]

Figure 26: The maximal mechanical power as a function of speed. No compensation(dotted), 50% compensated (dashed), 100% compensated (solid) and maximum poweroutput (dash-dotted) [3]

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Figure 27: The maximal mechanical power with 50% compensation at rated speed(dashed) and power production by a wind turbine (solid) [3]

flux density. The total emf in the stator winding is es, which is proportional to the fluxlinkage of the stator.

The compensation level is defined as the relative size of the generators totalinductance, (L + Lm). This is the same as the percentage of the generators reactive

power consumption which is produced by the series compensation. Figure 25 showsphasor diagram for different compensation levels. As seen from the figure, the anglebetween the induced voltage EPM and the current Idecreases when the generator speedincreases. [3]

However, the compensation level change when the generator speed change, asexplained earlier. The generator reactance decreases and the capacitor reactanceincrease when the generator speed decreases. Consequently, the level of compensationincreases and the generator will be overcompensated at low speed. Over compensationwill reduce the maximum power production for low speed in the same way as undercompensation for high generator speeds. As mention, to have a maximum power

output from the generator, the current I has to be in phase with EPM . This is equal to100% compensation. If the generator is overcompensated (over 100% compensation),the current I is before the induced voltage EPM , causing the maximum power todecrease. [3]

In Figure 26, the maximum mechanical power of the generator, as a function ofgenerator speed, is plotted for different compensation levels. Full compensation atrated speed leads to the highest power at rated speed, shown as solid. However, asthe speed decreases, the maximal generator power is quickly reduced because of thegenerator being more and more overcompensated. If the turbine is half compensatedat rated speed, shown as dashed, the maximal power decreases slower when the

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generator slows down. If no reactive compensation is used, the maximal power for thehighest generator speed is reduced to about half of the maximum power with reactive

compensation. [3]Figure 27 shows the maximum mechanical power of a generator with 50%

compensation at rated power and the power produced by the wind turbine. As seenfrom the figure, the power produced is lower than the maximum mechanical power forall generator speeds. [3]

The maximum power output from the generator is achieved when the current Iis inphase with EPM . However, it is more likely that a generator with high inductance willbe controlled to keep the absolute value of ES equal to the absolute value ofEPM . Theflux leakage of the stator is proportional to ES so a smaller compensation level allows asmaller generator design. In this case, the stator flux linkage equals the no-load value.

[3] 50% compensation is therefore used in the simulations.To minimize the losses in the generator, the current and the magnetic flux should be

minimized. They are both causing losses, which is usually the main limiting factor inlarge electrical machines. The core losses are much lower than the copper losses in a lowspeed generator and are therefore neglected in this model. The induced voltage ePM isassumed to be sinusoidal because the harmonics content is only a few percents of thetotal voltage. This means that the current harmonics cannot contribute to the producedpower. [3]

The size of the capacitors can be changed to change the compensation level when therotating speed increases or decreases. This will make the power output from the turbine

as high as possible for all rotating speeds. The variations must be done in steps, and asfew steps as possible because each step increase the system costs. One possibility is tohave a 100% compensation level for rated speed. When the speed decreases to a certainlevel, the size of the total capacitor increases so that the compensation level becomes100% for this generator speed. [3]

There are two ways of connecting the capacitors: in parallel or in series. A switch isneeded to disconnect one of the capacitors. If a parallel connection is used, the secondcapacitor has to be connected to increase the capacitance, since the total capacitance isthe sum of the two capacitors, as shown in Equation (12). C1 has to be dimensioned formaximal current and voltage at rated speed. C2 can be dimensioned for a lower current.

Ctot = C1 + C2 (12)

If the capacitors are connected in series, the second capacitor has to be disconnectedto increase the capacitance, since the total capacitance is given in Equation (13). C1 cantherefore be dimensioned for some lower voltage than for the alternative with parallelconnection. The current rating will be the same.

Ctot =C1 C2

C1 + C2(13)

The generator currents depend on whether the diode rectifier is connected to a

29


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voltage stiff or to a current stiff DC-link. If a current stiff DC-link is used, the currentgoing into the generator will be nearly square, resulting in harmonics and lower

maximum power output. It is only the fundamental current component which producesactive power while the limited rated current is the rms-value of the current, includingthe harmonics. Therefore the harmonics should be reduced to increase the maximalpower output and reduce the losses.

Figure 28: Phase diagram for series connected capacitors

Figure 28 shows the phase diagram for a PMSG with series connected capacitors. Itis assumed that all currents and voltages are sinusoidal; no harmonics appears. As seenfrom the figure, the angle between the induced voltage and the generator current canbe reduced by selecting a suitable value of the capacitor. If the capacitance is to low, the

induced voltage will have a negative angle compared to the generator current, and thesystem will be overcompensated.Equations (14) to (18) are used to calculate the generator current as a function of the

output voltage. In Equations (14) and (15) the real and imaginary part of the inducedvoltage Ef is found from the phase diagram. This is used to find the absolute value ofEf in (16). A second order expression for the generator current I is found in Equation(17) and the generator current is expressed in Equation (18).

Ef,re = U+ RI (14)

Ef,im = XI (15)

E2f = E2f,re + E

2f,im (16)

(R +L) I2 + 2RU I+ U2 E2 = 0 (17)

I =2UR +

(2UR)2 4 (R +e L) (U2 EPM2)

2 (R +e L)(18)

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Some simple tests using these equations are performed in MatLab. The machinedata for the 55kW PMSG in Vindlabben is used. These are shown in Table 6. The

result is shown in Figures 29, 31 and 30. All voltages and currents are assumed to besinusoidal. When a diode rectifier is used, this will not be the case. The DC-link voltageis also assumed to be proportional to the voltage on the input of the diode rectifier.

1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

x 103

0

5

10

15x 10

4

Capacitor size [F]

Power[W]

Generator power

1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

x 10

3

0

100

200

300

400

Capacitor size [F]

Voltage[V]/Current[A]

Load voltage U

Generator current IL

Figure 29: Maximum power [W] with respectively load voltage [V] and generatorcurrent [A] as a function of capacitor size

Figure 29 shows the maximum power output with respectively load voltage andgenerator current for increasing capacitor size. If the capacitor is less than 2300F, thegenerator is overcompensated at a generator frequency at 50Hz. If the capacitor is larger,the generator is undercompensated, as wanted. For a capacitor size of about 2300F,the sum of the generator synchronous reactance and the reactance of the capacitor is

about zero. This will allows a very large current to flow through the generator, becauseonly the resistance of the generator windings limits the current. The generator power isalso high, due to the high current. The generator current can be reduced by increasingthe load voltage.

Figure 30 shows the maximum power output with respectively load voltage andgenerator current as a function of generator frequency. As seen the generator power isvery low for low frequencies, however, the turbine power is also low because of the lowwind speed. The total reactance is almost zero when the generator frequency is 33Hz.

Figure 31 shows the power output and the generator current at 50Hz generatorfrequency as a function of the load voltage. As seen from the figure, the current

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5 10 15 20 25 30 35 40 45 500

2

4

6

8

10x 10

4

Generator frequency [Hz]

Power[W]

0 10 20 30 40 500

100

200

300


Voltage[V]/C

urrent[A]

Generator power

Load voltage U

Induced voltage Ef


Figure 30: Maximum power [W] with respectively load voltage [V] and generatorcurrent [A] as a function of generator frequency

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is actually decreasing when the generator power increases. The maximum power isreached for a relatively low load voltage.

4.4 PMSG with diode rectifier and parallel compensation

Figure 32: Schematic diagram of PM generator system. (a) With DC-DC buck converter,(b) With DC-DC boost converter [24]

The reactive power absorb by the permanent magnet synchronous generator couldalso be compensated with conductors in parallel with the generator. Figure 32 showsa schematic diagram for a PM generator with parallel compensated stator windings,diode rectifier and DC-DC converter. The power limit imposed by the series reactanceleads to poor utilisation and leaves little torque margin to cope with transient torquedue to wind gusts. Therefore, some form of compensation is needed, particularly athigh speed. [32]

Use of parallel capacitors raises the power capacity, but causes increased loss. Witha parallel capacitor, the peak power capability into a resistive load is increased by the

factor given by Equation (19). This means that any desired power can be delivered withappropriate choice of capacitors. [32]

1

1 2L/C (19)The reactive power produced by the generator in one phase is given by Equation

(20). The reactive power consumed by the capacitance per phase is given by Equation(21). As seen from the equations, both the reactive power produced by the generatorand the reactive power consumed by the capacitor increase linearly to the generatorfrequency.

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Qgen = Xgen I2

gen = Lgen I2 (20)

Qca p =U2ca p,phase

Xcap= CphaseU

2cap,phase (21)

As the wind speed increase, both the generator current Igen and the capacitor voltageUca p,phase will increase. The induced voltage Ef is proportional to the rotation speed andthe electrical frequency. This means that the capacitor has little effect at low frequenciesand speeds, but increasingly draws additional current as the frequency increases. [8]

Figure 33: Phase diagram for parallel connected capacitators

Ef,re = U+ RI XIC (22)

Ef,im = RIC + XI (23)

E2f = E2f,re + E

2f,im (24)

R2 + (L)2 I

2 + 2RU I+ U2E2f +4L2C2U222LCU2 = 0 (25)

I =2RU+

(2RU)2 4

R2 + (L)2

U2E2f +

4L2C2U222LCU2

2

R2 + (L)2 (26)

Figure 33 and Equations (22) to (26) show how the current is found when thegenerator voltage and the induced voltage is know. It is assumed that all voltage andcurrents are sinusoidal. In Equations (22) and (23) the real and imaginary part of theinduced voltage Ef are found from the phase diagram, Figure 33. The absolute value of

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Ef is found in (24) and this is used to find a second order expression for the generatorcurrent I, Equation (25). Now the current can be found as shown in Equation (26).

Some simple calculations using the equations for parallel compensated PMSG arealso performed in MatLab. The assumptions and machine data are the same as for theMatLab calculations of the series compensated system. The result is shown in Figures34, 35 and 36.

0 0.5 1 1.5 2

x 103

0

2

4

6

8x 10

5

X: 0.00144Y: 3.124e+005

Capacitor size [F]

Power[W]

0 0.5 1 1.5 2x 10

3

0

200

400

600

800

Capacitor size [F]


Generator power

Generator output voltage U


Figure 34: Maximum power [W] with respectively load voltage [V] and generatorcurrent [A] as a function of capacitor size

Figure 34 shows the maximum power output with respectively load voltage andgenerator current for increasing capacitor size. As seen, the generator voltage andturbine power increase when the generator power increase, while the generator currentis more or less constant until the capacitor size is about 1500F. The capacitor size used

in the laboratory is therefore chosen to be 1440F.Figure 35 shoes the generator power as a function of the generator voltage when the

turbine is operating at nominal speed. The generator current is decreasing when thevoltage increases, and the generator power will have a maximum when the generatorvoltage is 316V.

The maximum generator power is plotted as a function of generator frequency inFigure 36. As seen, both the generator current and generator voltage is increasing linearto the generator frequency.

A permanent magnet synchronous generator with a diode rectifier and parallelconnected capacitors is suggested in [32]. Some simulations on the equivalent circuit

36


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0 50 100 150 200 250 300 350 400 4500

1

2

3

4x 10

5

X: 316Y: 3.124e+005

Generator voltage [V]

Power[W]

0 50 100 150 200 250 300 350 400 450200

300

400

500

Generator voltage [V]

Voltage[V]/C

urrent[A]

Generator power


Figure 35: Maximum power [W] with respectively generator current [A] as a functionof load voltage

37


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0 10 20 30 40 500

2

4

6

8

10

12 x 10

4


Power[W]

0 10 20 30 40 500

100

200

300

400



Generator power

Generator output voltage U

Induced voltage Ef


Figure 36: Maximum power [W] with respectively load voltage [V] and generatorcurrent [A] as a function of generator frequency

Figure 37: Equivalent circuit including capacitor [32]

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Figure 38: Simulated currents with capacitor [32]

shown in Figure 37 are performed. The results are shown in Figure 38; The upper graph

shows the generator current, the middle shows the current going into the diode rectifierand the lowest shows the capacitor current. When the capacitor voltage exceeds theDC-link voltage, the diode begins to conduct. At this point the capacitor voltage isclamped to the DC-link voltage and the capacitor current becomes zero. The coil currentcontinues to flow and diverts into the DC-link. The subsequent behaviour of the currentis determined by the LR circuit and the DC and AC voltages with finite initial current.[32]

Figure 39 shows power as a function of DC voltage for different sizes of capacitors;0F, 100F, 200F and 400F. The lines show the simulated power and the pointsshow the measured power. As the size of the capacitor increases, the maximum power

output also increases. As seen from the figure, the power will increase when the DC-linkvoltage increase until a certain point where the power reaches its maximum. When theDC-link voltage is further increased, the current will decrease quicker than the voltageincreases, and the power output will decrease. [32] The generator is then operatingon the right side of the power curve where the generator power is decreasing withincreasing generator voltage.

The AC capacitors partly compensate the effect of the generator inductance,resulting in higher voltage and power. However, the compensation must not be takentoo far because of the danger that resonance might leads to damaging high voltage.The worst case is if a loss of grid connection leads to acceleration of the generator. The

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Figure 39: Power versus DC voltage for different capacitor sizes [32]

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pitch control will use some time to stop the turbine. Meanwhile, the frequency of thegenerator will increase towards resonance between the generator impedance and the

capacitors. The resulting high capacitor current passing through the coil might lead todemagnetisation of rotor modules if the capacitor or rectifier does not fail first. [32] Thisproblem will probably not appear in a large wind turbines due to the large moment ofinertia. The acceleration of the turbine will therefore be small before the pitch-controllerstarts to reduce the speed of the turbine.

Spooner and Chen suggest in [32] that each coil in the permanent magnetsynchronous generator may be connected individually to a single-phase rectifier bridge.This will make the complex interconnections of a three-phase winding unnecessary andthe DC-link voltage will have very little ripple because of the large number of phases.Thereby, a DC-link filter may not be needed. [32]

4.5 Passive filters for reducing current harmonics

Passive filters can be used for reducing current harmonics. However, the passivefilters have some drawbacks. The filtering characteristics are strongly affected by thesource impedance. Due to the resonant nature of passive filters there may be unwantedresonant interactions with the supply system. This affect can be avoided if the filters areoff-tuned or damping is added. The filter also causes additional losses. Active filtersalso have also some drawbacks. It is difficult to construct a large-rated current sourcewith a rapid current response. They have also high initial cost and running costs. [30]

Figure 40: Shunt configuration of harmonic trap filters [30]

A classical harmonic trap filter, as show in Figure 40 can be used for harmonicelimination. The main disadvantage with this filter is that is has to be tuned for anelectrical frequency. The wind turbine rotation speed is changing with the wind speed,and thereby also the frequency of the voltages and currents from the generator. Thetrap filter can be tuned for one wind speed, but it will not work properly for other windspeeds and rotation speeds. It is also need for one filter per harmonic which should befiltered. The size of the inductor L, the capacitor Cn and the resistor R is decided byEquations (27) to (29). [30]

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n fe,1 =1

2LCn(27)

Q =X0R

(28)

X0 =

L

Cn(29)

n fe,1 is the tuned frequency in nth order of the fundamental and the Q factor is

determined by R, L and Cn. The value varies from 30 to 60. Figure 40 also showsdamped filters. They provide low impedance for a wide spectrum of harmonics without

the need of subdivision of parallel branches. The behaviour of the damped filter is givenby two parameters given in Equations (30) and (31). Typical m values vary from 0.5 to2. [30]

F0 =1

2CR(30)

m =L

R2C(31)

Figure 41: Summary of line current THD content [30]

Figure 41 and 42 shows the total harmonic distortion for diode and thyristor rectifierwith harmonic trap filters tuned at different wind speeds. It shows that the solutionwith a diode rectifier and harmonic trap filter tuned at a wind speed of 7m/s gives

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Figure 42: Summary of line to line voltage THD content [30]

the least current THD and voltage THD. The figure also shows, not surprisingly, thatthe THD generated from a thyristor rectifier is larger then from a diode rectifier. Thedisadvantage with the harmonic trap filters is that a lot of energy is lost in the filter.

The generator losses are about 10% lower with harmonic trap filters. However the totallosses are some higher, according to [30].

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4.6 Active shunt filter for reducing current harmonics

Figure 43: Basic diagram of WECS with active shunt system [25]

An active shunt filter (ASF) for harmonic mitigation in wind turbines generators ispresent in [25]. Figure 43 shows the basic diagram of the system. The ASF controls thefilter current to actively shape the generator current into the sinusoid. With this activefilter the THD of the generator current is reduced from 10.68% to 2.60%. The harmoniccontent of the PMSG output voltage is also reduced, from 29.15% to 20.77%.

Figure 44: Block diagram of the ASF harmonic currents calculation and vDC voltagecontrol [25]

The control system of the ASF is described in [25]. The block diagram of the ASFharmonic current calculation is shown in Figure 44. The current is transformed from

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three-phase to the frame and then to the d-q frame and id and iq are filtered witha low pass filter.

The DC bus nominal voltage VDC must be greater than or equal to the line-to-linevoltage peak to actively control the current going into the filter. In order to maintain theDC bus voltage, an amount of active current must be delivered to the ASF. Therefore aPI-regulator is used to control id. The d-q current is then transformed to the frameand then to three-phase current. This is compared to the actual generator current andused as a reference to the active filter current.

Figure 45: PWM carrier control for ASF current [25]

Figure 45 shows how the voltage source inverter is controlled. The filter referencecurrent is compared to the actual filter current for each of the three phases and theswitching of the IGBTs is controlled by a PI-regulator and a PWM carrier strategy.

The filter inductance LF and the capacitor size CDC must be chosen properly. Apractical choice of LF guarantees that the active filter can generate a current with a

slope equal to the maximum slope of the load current. The ability to track the desiredsource current improves if the filter inductance is smaller. However, a smaller filterinductance requires a higher switching frequency to keep the ripple in the line currentacceptably small. The capacitor size is decided based on the filter current IF and themaximum accepted voltage ripple vDCmax. Power losses in the ASF consist of losses inthe passive parts such as the inductors and the capacitor and losses in the active parts,the IGBTs. The simulations performed in [25] shows that the total electrical efficiency is88.05% for the system without AFT and 84.74% with AFT. The ASF losses are 3%. Therectifier and PMSG copper losses also increase when the AFT is used.

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5 Control systems

The swaying of an offshore floating wind turbine has to be controlled to reduce themechanical forces on the tower and to prevent the tower to tip. Therefore the thrustforce exerted on the blades has to be controlled. Besides the wind speed, the pitch angleand the turbine rotating speed affects this force. Since the moment of inertia of the rotoris quite large, the time constant of the rotation speed is also large. The rotation speeddo also affects the power coefficient cp of the turbine. A small difference between theactual rotation speed and the optimal rotation speed results in a relative large decreasein power production.

The pitch angle can be controlled much faster than the rotation speed. It is thereforemuch more suitable for controlling the swaying of the wind turbine. However, the

power coefficient cp is also decreasing when the pitch angle differ from its ideal value.The pitch angle should therefore be used to control the swaying of the wind turbineand to reduce the turbine power when the turbine power exceeds the rated power. Thegenerator torque should be used to control the speed of the rotor. Some regulationstrategies for speed control are present in the following chapters.

5.1 Speed and torque control

Figure 46: Wind generator power curves at various wind speeds. [7]

The turbine rotation speed is important to obtain a maximum power production.Figure 46 shows the turbine power curves for various wind speeds. The optimal powerproduction line is also drawn. This is the rotation speed which gives the maximum

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5 CONTROL SYSTEMS

output power for different wind speeds. The value of the tip-speed ratio is constantfor all maximum power points, while the turbine rotation speed is related to the wind

speed as given in Equation (32).[7]

n = optVnR

(32)

Two types of tracking algorithms (MPPT) exist; Methods based on the knowledge onthe Cp () characteristic and methods allowing to seek the optimal operation withoutknowing the turbine characteristic.

5.1.1 MPPT with knowledge of the turbine characteristic

Three different tracking algorithms for systems with known turbine characteristic willbe mention here; speed control, torque control and a diode bridge with DC-DC chopperstructure. If speed control is used, the power curve is used to find the optimal speedreference versus power.

Tip-speed ratio control or speed control regulates the rotational speed of thegenerator to maintain an optimal tip-speed ratio, . The power curve is used to find theoptimal speed reference versus power. Both the wind speed and the rotational speedneed to be measured to calculate the tip-speed ratio. This will increase the system costand present difficulties in practical implementation. The optimal tip-speed ratio mustalso be known. This can vary from one wind turbine to another. A PWM controlledIGBT converter is used to control the turbine speed. [10] [4]

When torque control is used, the power curve is used to find the optimal torquereference. Optimal torque control adjusts the generator torque to an optimal one atdifferent wind speed. The optimal tip-speed ratio and generator parameters are needed,and the control precision depends on the precision of these variables. A PWM controlledIGBT rectifier is needed. [10] [4]

The third alternative is a diode AC-DC converter linked to a DC-DC chopper.Seeking the optimal operation can be achieved by controlling the load current by obtainan optimal load characteristic versus the DC voltage. The DC-link voltage is directlyrelated to the generator electromotive forces magnitude. These forces are proportionalto the turbine speed. The configuration is simple and inexpensive, with a low cost AC-

DC converter and a minimum of sensors. [4]According to [4], the structure including a diode converter with a DC-DC chopper is

a cheaper and simpler solution and the simulation results are quite satisfactory. Even ifthe tuning of the generator is indirect and highly slower, the high inertia of the turbineoperates as a filter, filtering the wind fluctuations. The relationship between the outputcurrent and the DC-link voltage at the output of the diode rectifier can be determinedby simulation and by experiment. This curve will include the system losses for anyoperation points. [4]

Figure 47 shows the overall control scheme of the wind turbine with anemometersensor. The anemometer is used to find the tip-speed ratio and provides the wind

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Figure 47: Block diagram of the WECS-controlled system with anemometer [13]

power reference to the MPPT controller. The input operating DC voltage reference canbe found by comparing this reference to the turbine power. This signal is fed into the

direct driven permanent magnet synchronous generators with diode rectifiers for use in offshore wind...

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